ANALYTICAL REPRESENTATION OF ANGULAR DISTRIBUTION DATA

Journal Article · Sun Jun 01 04:00:00 EDT 1958 · Journal of Applied Physics (U.S.)

DOI:https://doi.org/10.1063/1.1723339· OSTI ID:4338396

Snowdon, S C; Eisenbud, L; Marshall, J F

A simple method is presented for obtaining an analytical curve fitted to data points. The requirements in least squares analysis that yield a single best curve are relaxed to the extent that it is only necessary to choose one of many possible good fits. The subsequent analytical determination of this good curve nuay be obtained with relatively little computational effort. Specifically, the method is applied to an analytical representation of angular distribution data by means of a Legendre polynomial series. A smooth curve which one feels is statistically justified is drawn through the data points. The values of this curve at eleven points are chosen as the coefficients in a Lagrange interpolation function series. The intermediate points give back approximately the drawn curve and are also statistically adequate. Subsequent use of a transformation matrix between the Lagrange interpolation basis aad the Legendre polynomial basis fields the desired expansion. The transformation matrix is presented for the case in which an 11-point fit adequately characterizes the dath curve. Error estimates also are given. (auth)

• Research Organization: The Franklin Inst., Swarthmore, Penna.
• Sponsoring Organization: USDOE
• NSA Number: NSA-12-011587
• OSTI ID: 4338396
• Journal Information: Journal of Applied Physics (U.S.), Journal Name: Journal of Applied Physics (U.S.) Vol. Vol: 29; ISSN JAPIA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ANGULAR DISTRIBUTION
DIFFERENTIAL EQUATIONS
LEAST SQUARES
LEGENDRE FUNCTIONS
MATHEMATICS
MATRICES
MOTION
PHYSICS